Finite Group Databasebeta

← #31065140

Subgroups — #31065140

Order 17152.

2078 conjugacy classes of subgroups.

The subgroup lattice has 1628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22568527C211yesmaximal, characteristic, complemented
2#22568518C211yesmaximal, characteristic, complemented
3#22568054C211yesmaximal, characteristic, complemented
4#22567931C211yesmaximal, characteristic, complemented
5#22567545C211yesmaximal, characteristic, complemented
6#22567311C211yesmaximal, characteristic, complemented
7#22567258C211yesmaximal, characteristic, complemented
8#22567121C211yesmaximal, characteristic, complemented
9#22566963C211yesmaximal, characteristic, complemented
10#22566962C211yesmaximal, characteristic, complemented
11#22566916C211yesmaximal, characteristic, complemented
12#22566896C211yesmaximal, characteristic, complemented
13#22566882C211yesmaximal, characteristic, complemented
14#22566877C211yesmaximal, characteristic, complemented
15#22566755C211yesmaximal, characteristic, complemented
16#22566696C211yesmaximal, characteristic, complemented
17#22566556C211yesmaximal, characteristic, complemented
18#22566019C211yesmaximal, characteristic, complemented
19#22565983C211yesmaximal, characteristic, complemented
20#22564453C211yesmaximal, characteristic, complemented
21#22564346C211yesmaximal, characteristic, complemented
22#22564013C211yesmaximal, characteristic, complemented
23#22563876C211yesmaximal, characteristic, complemented
24#22563674C211yesmaximal, characteristic, complemented
25#22563603C211yesmaximal, characteristic, complemented
26#22563578C211yesmaximal, characteristic
27#22563533C211yesmaximal, characteristic, complemented
28#22562862C211yesmaximal, characteristic, complemented
29#22562822C211yesmaximal, characteristic, complemented
30#390×D67C211yesmaximal, characteristic, complemented
31C67×#2694C211yesmaximal, characteristic, complemented
32C22×D4×D67C2211yescharacteristic
33C2×#14524038C2211yescharacteristic, complemented
34C2×#14524036C2211yescharacteristic, complemented
35C2×#14524034C2211yescharacteristic, complemented
36C2×#14524028C2211yescharacteristic, complemented
37C2×#14524027C2211yescharacteristic, complemented
38C2×#14524026C2211yescharacteristic
39C2×#14524023C2211yescharacteristic, complemented
40C2×#14524021C2211yescharacteristic
41C2×#14524021C2211yescharacteristic, complemented
42C2×#14524018C2211yescharacteristic
43C2×#14524016C2211yescharacteristic
44C2×#14524013C2211yescharacteristic
45C2×#14524013C2211yescharacteristic
46C2×#14524005C2211yescharacteristic
47C2×C4⋊C4×D67C2211yescharacteristic
48C22×(C2×D67)⋊C4C2211yescharacteristic
49C2×C22⋊C4×D67C2211yescharacteristic
50C2×C22⋊C4×D67C2211yescharacteristic
51C2×C22⋊C4×D67C2211yescharacteristic
52C2×C22⋊C4×D67C2211yescharacteristic
53C2×C22⋊C4×D67C2211yescharacteristic
54C2×C42×D67C2211yescharacteristic
55#16863335C2211yescharacteristic, complemented
56#16863332C2211yescharacteristic, complemented
57#16863331C2211yescharacteristic, complemented
58#16863331C2211yescharacteristic, complemented
59#16863329C2211yescharacteristic, complemented
60#16863327C2211yescharacteristic, complemented
61#16863326C2211yescharacteristic, complemented
62#16863325C2211yescharacteristic, complemented
63#16863324C2211yescharacteristic, complemented
64#16863323C2211yescharacteristic, complemented
65#16863323C2211yescharacteristic, complemented
66#16863323C2211yescharacteristic, complemented
67#16863323C2211yescharacteristic, complemented
68#16863322C2211yescharacteristic, complemented
69#16863321C2211yescharacteristic, complemented
70#16863321C2211yescharacteristic, complemented
71#16863320C2211yescharacteristic, complemented
72#16863319C2211yescharacteristic, complemented
73#16863319C2211yescharacteristic, complemented
74#16863319C2211yescharacteristic, complemented
75#16863318C2211yescharacteristic, complemented
76#16863318C2211yescharacteristic, complemented
77#16863318C2211yescharacteristic, complemented
78#16863316C2211yescharacteristic, complemented
79#16863314C2211yescharacteristic, complemented
80#16863313C2211yescharacteristic
81#16863313C2211yescharacteristic
82#16863313C2211yescharacteristic, complemented
83#16863313C2211yescharacteristic, complemented
84#16863313C2211yescharacteristic, complemented
85#16863313C2211yescharacteristic, complemented
86#16863312C2211yescharacteristic, complemented
87#16863312C2211yescharacteristic, complemented
88#16863311C2211yescharacteristic
89#16863311C2211yescharacteristic
90#16863311C2211yescharacteristic
91#16863311C2211yescharacteristic, complemented
92#16863309C2211yescharacteristic, complemented
93#16863308C2211yescharacteristic, complemented
94#16863308C2211yescharacteristic, complemented
95#16863305C2211yescharacteristic
96#16863304C2211yescharacteristic
97#16863299C2211yescharacteristic
98#16863298C2211yescharacteristic
99#16863298C2211yescharacteristic, complemented
100#16863297C2211yescharacteristic
101#16863296C2211yescharacteristic
102#16863296C2211yescharacteristic
103#16863296C2211yescharacteristic
104#16863296C2211yescharacteristic
105#16863296C2211yescharacteristic, complemented
106#16863294C2211yescharacteristic, complemented
107#16863293C2211yescharacteristic, complemented
108#16863291C2211yescharacteristic, complemented
109#16863289C2211yescharacteristic, complemented
110#16863288C2211yescharacteristic, complemented
111#16863288C2211yescharacteristic, complemented
112#16863287C2211yescharacteristic, complemented
113#16863287C2211yescharacteristic, complemented
114#16863286C2211yescharacteristic, complemented
115#16863286C2211yescharacteristic, complemented
116#16863285C2211yescharacteristic, complemented
117#16863285C2211yescharacteristic, complemented
118#16863284C2211yescharacteristic, complemented
119#16863283C2211yescharacteristic, complemented
120#16863282C2211yescharacteristic, complemented
121#16863282C2211yescharacteristic, complemented
122#16863282C2211yescharacteristic, complemented
123#16863280C2211yescharacteristic, complemented
124#16863279C2211yescharacteristic, complemented
125#16863278C2211yescharacteristic, complemented
126#16863278C2211yescharacteristic, complemented
127#16863278C2211yescharacteristic, complemented
128#16863276C2211yescharacteristic
129#16863275C2211yescharacteristic, complemented
130#16863274C2211yescharacteristic
131#16863274C2211yescharacteristic
132#16863274C2211yescharacteristic
133#16863274C2211yescharacteristic
134#16863274C2211yescharacteristic
135#16863274C2211yescharacteristic, complemented
136#16863273C2211yescharacteristic
137#16863272C2211yescharacteristic
138#16863272C2211yescharacteristic, complemented
139#16863272C2211yescharacteristic, complemented
140#16863270C2211yescharacteristic
141#16863270C2211yescharacteristic
142#16863270C2211yescharacteristic
143#16863270C2211yescharacteristic
144#16863270C2211yescharacteristic, complemented
145#16863270C2211yescharacteristic, complemented
146#16863270C2211yescharacteristic, complemented
147#16863267C2211yescharacteristic
148#16863267C2211yescharacteristic
149#16863267C2211yescharacteristic
150#16863267C2211yescharacteristic
151#16863267C2211yescharacteristic
152#16863267C2211yescharacteristic
153#16863267C2211yescharacteristic, complemented
154#16863267C2211yescharacteristic, complemented
155#16863267C2211yescharacteristic, complemented
156#16863267C2211yescharacteristic, complemented
157#16863263C2211yescharacteristic, complemented
158#16863261C2211yescharacteristic, complemented
159#16863257C2211yescharacteristic, complemented
160#16863256C2211yescharacteristic, complemented
161#16863254C2211yescharacteristic, complemented
162#16863254C2211yescharacteristic, complemented
163#16863253C2211yescharacteristic
164#16863253C2211yescharacteristic
165#16863253C2211yescharacteristic
166#16863253C2211yescharacteristic, complemented
167#16863251C2211yescharacteristic
168#16863251C2211yescharacteristic
169#16863251C2211yescharacteristic
170#16863251C2211yescharacteristic
171C4×(C2×D67)⋊C4C2211yescharacteristic
172C2×#125×C67C2211yescharacteristic, complemented
173C2×#123×C67C2211yescharacteristic
174#399×C67C2211yescharacteristic, complemented
175#399×C67C2211yescharacteristic, complemented
176#398×C67C2211yescharacteristic, complemented
177#397×C67C2211yescharacteristic, complemented
178#396×C67C2211yescharacteristic, complemented
179#394×C67C2211yescharacteristic
180#390×C67C2211yescharacteristic
181#389×C67C2211yescharacteristic, complemented
182#388×C67C2211yescharacteristic, complemented
183#388×C67C2211yescharacteristic, complemented
184#387×C67C2211yescharacteristic, complemented
185#385×C67C2211yescharacteristic, complemented
186#380×C67C2211yescharacteristic, complemented
187C24×D67C2311yescharacteristic
188C24×D67C2311yescharacteristic
189C22×Dic134C2311yescharacteristic
190C22×D268C2311yescharacteristic
191C22×D268C2311yescharacteristic
192C22×D268C2311yescharacteristic
193C22×D268C2311yescharacteristic
194C22×C22⋊D67C2311yescharacteristic
195C22×C22⋊D67C2311yescharacteristic
196C22×C22⋊D67C2311yescharacteristic
197C22×C22⋊D67C2311yescharacteristic
198C2×D4×D67—24no—
199C2×D4×D67—42no—
200C2×D4×D67—42no—
201C23×Dic67C2311yescharacteristic
202C22×C4×D67C2311yescharacteristic
203C22×C4×D67C2311yescharacteristic
204C22×C4×D67C2311yescharacteristic
205C22×C4×D67C2311yescharacteristic
206C22×C4×D67C2311yescharacteristic
207C22×C4×D67C2311yescharacteristic
208C22×C4×D67C2311yescharacteristic
209C22×C4×D67C2311yescharacteristic
210#14524038—42no—
211#14524036—42no—
212#14524034—42no—
213#14524028—42no—
214#14524027—42no—
215#14524026—42no—
216#14524023—42no—
217#14524021—42no—
218#14524021—42no—
219#14524018—42no—
220#14524016—42no—
221#14524013—24no—
222#14524013—42no—
223#14524005—42no—
224C2×C4⋊Dic67C2311yescharacteristic
225C2×C4⋊Dic67C2311yescharacteristic
226C2×C4⋊Dic67C2311yescharacteristic
227C2×C4⋊Dic67C2311yescharacteristic
228C2×C4⋊Dic67C2311yescharacteristic
229C2×C4⋊Dic67C2311yescharacteristic
230C2×C4⋊Dic67C2311yescharacteristic
231C2×C4⋊Dic67C2311yescharacteristic
232C2×Dic67⋊C4C2311yescharacteristic
233C2×Dic67⋊C4C2311yescharacteristic
234C2×Dic67⋊C4C2311yescharacteristic
235C2×Dic67⋊C4C2311yescharacteristic
236C2×Dic67⋊C4C2311yescharacteristic
237C2×Dic67⋊C4C2311yescharacteristic
238C2×Dic67⋊C4C2311yescharacteristic
239C2×Dic67⋊C4C2311yescharacteristic
240C2×Dic67⋊C4C2311yescharacteristic
241C2×Dic67⋊C4C2311yescharacteristic
242C2×Dic67⋊C4C2311yescharacteristic
243C2×Dic67⋊C4C2311yescharacteristic
244C2×Dic67⋊C4C2311yescharacteristic
245C2×Dic67⋊C4C2311yescharacteristic
246C4⋊C4×D67—42no—
247C2×C22⋊Dic67C2311yescharacteristic
248C2×C22⋊Dic67C2311yescharacteristic
249C2×C22⋊Dic67C2311yescharacteristic
250C2×C22⋊Dic67C2311yescharacteristic
251C2×C22⋊Dic67C2311yescharacteristic
252C2×C22⋊Dic67C2311yescharacteristic
253C2×C22⋊Dic67C2311yescharacteristic
254C2×C22⋊Dic67C2311yescharacteristic
255C2×C22⋊Dic67C2311yescharacteristic
256C2×(C2×D67)⋊C4—24no—
257C2×(C2×D67)⋊C4C2311yescharacteristic
258C2×(C2×D67)⋊C4C2311yescharacteristic
259C2×(C2×D67)⋊C4C2311yescharacteristic
260C2×(C2×D67)⋊C4C2311yescharacteristic
261C2×(C2×D67)⋊C4C2311yescharacteristic
262C2×(C2×D67)⋊C4C2311yescharacteristic
263C2×(C2×D67)⋊C4C2311yescharacteristic
264C2×(C2×D67)⋊C4C2311yescharacteristic
265C2×(C2×D67)⋊C4C2311yescharacteristic
266C2×(C2×D67)⋊C4C2311yescharacteristic
267C2×(C2×D67)⋊C4C2311yescharacteristic
268C2×(C2×D67)⋊C4C2311yescharacteristic
269C2×(C2×D67)⋊C4C2311yescharacteristic
270C2×(C2×D67)⋊C4C2311yescharacteristic
271C2×(C2×D67)⋊C4C2311yescharacteristic
272C2×(C2×D67)⋊C4C2311yescharacteristic
273C2×(C2×D67)⋊C4C2311yescharacteristic
274C2×(C2×D67)⋊C4C2311yescharacteristic
275C2×(C2×D67)⋊C4C2311yescharacteristic
276C2×(C2×D67)⋊C4C2311yescharacteristic
277C2×(C2×D67)⋊C4C2311yescharacteristic
278C2×(C2×D67)⋊C4C2311yescharacteristic
279C2×(C2×D67)⋊C4C2311yescharacteristic
280C2×(C2×D67)⋊C4C2311yescharacteristic
281C2×(C2×D67)⋊C4C2311yescharacteristic
282C2×(C2×D67)⋊C4C2311yescharacteristic
283C2×(C2×D67)⋊C4C2311yescharacteristic
284C2×(C2×D67)⋊C4C2311yescharacteristic
285C2×(C2×D67)⋊C4C2311yescharacteristic
286C2×(C2×D67)⋊C4C2311yescharacteristic
287C2×(C2×D67)⋊C4C2311yescharacteristic
288C2×(C2×D67)⋊C4C2311yescharacteristic
289C2×(C2×D67)⋊C4C2311yescharacteristic
290C2×(C2×D67)⋊C4C2311yescharacteristic
291C2×(C2×D67)⋊C4C2311yescharacteristic
292C2×(C2×D67)⋊C4C2311yescharacteristic
293C22⋊C4×D67—42no—
294C22⋊C4×D67—42no—
295C22⋊C4×D67—42no—
296C22⋊C4×D67—42no—
297C22⋊C4×D67—42no—
298C2×C4×Dic67C2311yescharacteristic
299C2×C4×Dic67C2311yescharacteristic
300C2×C4×Dic67C2311yescharacteristic
301C2×C4×Dic67C2311yescharacteristic
302C2×C4×Dic67C2311yescharacteristic
303C42×D67—42no—
304C67⋊#95C2311yescharacteristic
305C67⋊#95C2311yescharacteristic
306C67⋊#95C2311yescharacteristic
307C67⋊#95C2311yescharacteristic
308C67⋊#95C2311yescharacteristic
309C67⋊#95C2311yescharacteristic
310C67⋊#95C2311yescharacteristic
311C67⋊#95C2311yescharacteristic
312C67⋊#95C2311yescharacteristic
313C67⋊#95C2311yescharacteristic
314C67⋊#95C2311yescharacteristic
315C67⋊#95C2311yescharacteristic
316C67⋊#95C2311yescharacteristic
317C67⋊#95C2311yescharacteristic
318C67⋊#95C2311yescharacteristic
319C67⋊#95C2311yescharacteristic
320C67⋊#95C2311yescharacteristic
321C67⋊#95C2311yescharacteristic
322C67⋊#95C2311yescharacteristic
323C67⋊#95C2311yescharacteristic
324C67⋊#95C2311yescharacteristic
325C67⋊#95C2311yescharacteristic
326C67⋊#95C2311yescharacteristic
327C67⋊#95C2311yescharacteristic
328C67⋊#95C2311yescharacteristic
329C67⋊#95C2311yescharacteristic
330C67⋊#95C2311yescharacteristic
331C67⋊#95C2311yescharacteristic
332C22×D4×C67C2311yescharacteristic
333C23×C4×C67C2311yescharacteristic
334#125×C67—42no—
335#123×C67—42no—
336C2×C4⋊C4×C67C2311yescharacteristic
337C2×C4⋊C4×C67C2311yescharacteristic
338C2×C4⋊C4×C67C2311yescharacteristic
339C2×C4⋊C4×C67C2311yescharacteristic
340C2×C4⋊C4×C67C2311yescharacteristic
341C2×C4⋊C4×C67C2311yescharacteristic
342C2×C4⋊C4×C67C2311yescharacteristic
343C2×C4⋊C4×C67C2311yescharacteristic
344C2×C4⋊C4×C67C2311yescharacteristic
345C2×C4⋊C4×C67C2311yescharacteristic
346C2×C4⋊C4×C67C2311yescharacteristic
347C2×C4⋊C4×C67C2311yescharacteristic
348C2×C22⋊C4×C67C2311yescharacteristic
349C2×C22⋊C4×C67C2311yescharacteristic
350C2×C22⋊C4×C67C2311yescharacteristic
351C2×C22⋊C4×C67C2311yescharacteristic
352C2×C22⋊C4×C67C2311yescharacteristic
353C2×C22⋊C4×C67C2311yescharacteristic
354C2×C22⋊C4×C67C2311yescharacteristic
355C2×C22⋊C4×C67C2311yescharacteristic
356C2×C22⋊C4×C67C2311yescharacteristic
357C2×C22⋊C4×C67C2311yescharacteristic
358C2×C22⋊C4×C67C2311yescharacteristic
359C2×C42×C67C2311yescharacteristic
360C2×C42×C67C2311yescharacteristic
361#95×C67C2311yescharacteristic
362#95×C67C2311yescharacteristic
363#95×C67C2311yescharacteristic
364#95×C67C2311yescharacteristic
365#95×C67C2311yescharacteristic
366#95×C67C2311yescharacteristic
367#95×C67C2311yescharacteristic
368#95×C67C2311yescharacteristic
369C23×D67—22no—
370C23×D67—22no—
371C23×D67—22no—
372C23×D67—22no—
373C23×D67—22no—
374C23×D67—41no—
375C23×D67—41no—
376C23×D67—41no—
377C23×D67—41no—
378C23×D67—41no—
379C23×D67—41no—
380C23×D67—41no—
381C23×D67—41no—
382C23×D67#4114yes—
383C23×D67C2411yescharacteristic
384C23×D67C2411yescharacteristic
385C23×D67C2411yescharacteristic
386C23×D67C2411yescharacteristic
387C2×Dic134—41no—
388C2×Dic134—41no—
389C2×Dic134—41no—
390C2×D268—22no—
391C2×D268—22no—
392C2×D268—22no—
393C2×D268—22no—
394C2×D268—22no—
395C2×D268—22no—
396C2×D268—41no—
397C2×D268—41no—
398C2×D268—41no—
399C2×D268—41no—
400C2×D268—41no—
401C2×D268—41no—
402C2×C22⋊D67—22no—
403C2×C22⋊D67—22no—
404C2×C22⋊D67—22no—
405C2×C22⋊D67—22no—
406C2×C22⋊D67—22no—
407C2×C22⋊D67—41no—
408C2×C22⋊D67—41no—
409C2×C22⋊D67—41no—
410C2×C22⋊D67—41no—
411C2×C22⋊D67—41no—
412C2×C22⋊D67—41no—
413C2×C22⋊D67—41no—
414D4×D67—416no—
415C22×Dic67—22no—
416C22×Dic67—41no—
417C22×Dic67—41no—
418C22×Dic67C2411yescharacteristic
419C22×Dic67C2411yescharacteristic
420C22×Dic67C2411yescharacteristic
421C22×Dic67C2411yescharacteristic
422C22×Dic67C2411yescharacteristic
423C22×Dic67C2411yescharacteristic
424C22×Dic67C2411yescharacteristic
425C22×Dic67C2411yescharacteristic
426C22×Dic67C2411yescharacteristic
427C22×Dic67C2411yescharacteristic
428C22×Dic67C2411yescharacteristic
429C22×Dic67C2411yescharacteristic
430C2×C4×D67—22no—
431C2×C4×D67—22no—
432C2×C4×D67—22no—
433C2×C4×D67—22no—
434C2×C4×D67—22no—
435C2×C4×D67—22no—
436C2×C4×D67—22no—
437C2×C4×D67—22no—
438C2×C4×D67—41no—
439C2×C4×D67—41no—
440C2×C4×D67—41no—
441C2×C4×D67—41no—
442C2×C4×D67—41no—
443C2×C4×D67—41no—
444C2×C4×D67—41no—
445C2×C4×D67—41no—
446C2×C4×D67—41no—
447C2×C4×D67—41no—
448C2×C4×D67—41no—
449C2×C4×D67—41no—
450C2×C4×D67—41no—
451C2×C4×D67—41no—
452C2×C4×D67—41no—
453C2×C4×D67—41no—
454C4⋊Dic67—22no—
455C4⋊Dic67—22no—
456C4⋊Dic67—41no—
457C4⋊Dic67—41no—
458C4⋊Dic67—41no—
459C4⋊Dic67—41no—
460C4⋊Dic67—41no—
461C4⋊Dic67—41no—
462Dic67⋊C4—22no—
463Dic67⋊C4—22no—
464Dic67⋊C4—22no—
465Dic67⋊C4—22no—
466Dic67⋊C4—41no—
467Dic67⋊C4—41no—
468Dic67⋊C4—41no—
469Dic67⋊C4—41no—
470Dic67⋊C4—41no—
471Dic67⋊C4—41no—
472Dic67⋊C4—41no—
473Dic67⋊C4—41no—
474Dic67⋊C4—41no—
475Dic67⋊C4—41no—
476C22⋊Dic67—41no—
477C22⋊Dic67—41no—
478C22⋊Dic67—41no—
479C22⋊Dic67—41no—
480C22⋊Dic67—41no—
481C22⋊Dic67—41no—
482C22⋊Dic67—41no—
483C22⋊Dic67—41no—
484C22⋊Dic67—41no—
485(C2×D67)⋊C4—22no—
486(C2×D67)⋊C4—22no—
487(C2×D67)⋊C4—22no—
488(C2×D67)⋊C4—22no—
489(C2×D67)⋊C4—22no—
490(C2×D67)⋊C4—22no—
491(C2×D67)⋊C4—22no—
492(C2×D67)⋊C4—22no—
493(C2×D67)⋊C4—22no—
494(C2×D67)⋊C4—22no—
495(C2×D67)⋊C4—22no—
496(C2×D67)⋊C4—22no—
497(C2×D67)⋊C4—22no—
498(C2×D67)⋊C4—22no—
499(C2×D67)⋊C4—22no—
500(C2×D67)⋊C4—41no—
501(C2×D67)⋊C4—41no—
502(C2×D67)⋊C4—41no—
503(C2×D67)⋊C4—41no—
504(C2×D67)⋊C4—41no—
505(C2×D67)⋊C4—41no—
506(C2×D67)⋊C4—41no—
507(C2×D67)⋊C4—41no—
508(C2×D67)⋊C4—41no—
509(C2×D67)⋊C4—41no—
510(C2×D67)⋊C4—41no—
511(C2×D67)⋊C4—41no—
512(C2×D67)⋊C4—41no—
513(C2×D67)⋊C4—41no—
514(C2×D67)⋊C4—41no—
515(C2×D67)⋊C4—41no—
516(C2×D67)⋊C4—41no—
517(C2×D67)⋊C4—41no—
518(C2×D67)⋊C4—41no—
519(C2×D67)⋊C4—41no—
520(C2×D67)⋊C4—41no—
521C4×Dic67—22no—
522C4×Dic67—22no—
523C4×Dic67—41no—
524C4×Dic67—41no—
525C4×Dic67—41no—
526C24×C67C2411yescharacteristic
527C24×C67C2411yescharacteristic
528C2×D4×C67—22no—
529C2×D4×C67—22no—
530C2×D4×C67—41no—
531C22×C4×C67—22no—
532C22×C4×C67—41no—
533C22×C4×C67—41no—
534C22×C4×C67C2411yescharacteristic
535C22×C4×C67C2411yescharacteristic
536C22×C4×C67C2411yescharacteristic
537C22×C4×C67C2411yescharacteristic
538C22×C4×C67C2411yescharacteristic
539C22×C4×C67C2411yescharacteristic
540C22×C4×C67C2411yescharacteristic
541C22×C4×C67C2411yescharacteristic
542C22×C4×C67C2411yescharacteristic
543C22×C4×C67C2411yescharacteristic
544C22×C4×C67C2411yescharacteristic
545C22×C4×C67C2411yescharacteristic
546C22×C4×C67C2411yescharacteristic
547C4⋊C4×C67—22no—
548C4⋊C4×C67—22no—
549C4⋊C4×C67—22no—
550C4⋊C4×C67—22no—
551C4⋊C4×C67—22no—
552C4⋊C4×C67—41no—
553C4⋊C4×C67—41no—
554C4⋊C4×C67—41no—
555C4⋊C4×C67—41no—
556C4⋊C4×C67—41no—
557C4⋊C4×C67—41no—
558C4⋊C4×C67—41no—
559C22⋊C4×C67—22no—
560C22⋊C4×C67—22no—
561C22⋊C4×C67—22no—
562C22⋊C4×C67—41no—
563C22⋊C4×C67—41no—
564C22⋊C4×C67—41no—
565C22⋊C4×C67—41no—
566C22⋊C4×C67—41no—
567C22⋊C4×C67—41no—
568C22⋊C4×C67—41no—
569C22⋊C4×C67—41no—
570C42×C67—41no—
571C42×C67—41no—
572C23×C67—21no—
573C23×C67—21no—
574C23×C67—21no—
575C23×C67—21no—
576C23×C67—21no—
577C23×C67—21no—
578C23×C67—21no—
579C23×C67—21no—
580C23×C67—21no—
581C23×C67—21no—
582C23×C67—21no—
583C23×C67—21no—
584C23×C67—21no—
585C23×C67C2×#4112yes—
586C23×C67C2511yescharacteristic
587C22×D67—21no—
588C22×D67—21no—
589C22×D67—21no—
590C22×D67—21no—
591C22×D67—21no—
592C22×D67—21no—
593C22×D67—21no—
594C22×D67—21no—
595C22×D67—21no—
596C22×D67—21no—
597C22×D67—28no—
598C22×D67—21no—
599C22×D67—21no—
600C22×D67—21no—
601C22×D67—21no—
602C22×D67—21no—
603C22×D67—21no—
604C22×D67—21no—
605C22×D67—21no—
606C22×D67—21no—
607C22×D67—21no—
608C22×D67—21no—
609C22×D67—21no—
610C22×D67—21no—
611C22×D67—21no—
612C22×D67—44no—
613C22×D67—44no—
614C22×D67—44no—
615C22×D67—44no—
616C22×D67—44no—
617C22×D67—82no—
618C22×D67—82no—
619C22×D67—82no—
620C22×D67—82no—
621C22×D67—82no—
622C22×D67—82no—
623C22×D67—82no—
624C22×D67—82no—
625C22×D67C2×#4112yes—
626C22×D67C2×#4112yes—
627C22×D67H(5,𝔽2)12yes—
628C22×D672−1+412yes—
629D4×C67—44no—
630C2×C4×C67—21no—
631C2×C4×C67—21no—
632C2×C4×C67—21no—
633C2×C4×C67—21no—
634C2×C4×C67—21no—
635C2×C4×C67—21no—
636C2×C4×C67—21no—
637C2×C4×C67—21no—
638C2×C4×C67—21no—
639C2×C4×C67—21no—
640C2×C4×C67—21no—
641C2×C4×C67—21no—
642C2×C4×C67—21no—
643C2×C4×C67—21no—
644C2×C4×C67—21no—
645C2×C4×C67—21no—
646C2×C4×C67—21no—
647C2×C4×C67—21no—
648C2×C4×C67—21no—
649C2×C4×C67—21no—
650C2×C4×C67—21no—
651C2×C4×C67—21no—
652C2×C4×C67—21no—
653C2×C4×C67—21no—
654C2×C4×C67—21no—
655C2×C4×C67—21no—
656C2×C4×C67—21no—
657C2×C4×C67—21no—
658C2×C4×C67—21no—
659C2×C4×C67—21no—
660C2×C4×C67—21no—
661C2×C4×C67—21no—
662C2×C4×C67—21no—
663C2×C4×C67—21no—
664C2×C4×C67—21no—
665C2×C4×C67—21no—
666C2×C4×C67—21no—
667C2×C4×C67—82no—
668C2×C4×C67H(5,𝔽2)12yes—
669C2×C4×C67H(5,𝔽2)12yes—
670C22⋊D67—44no—
671C22⋊D67—44no—
672C22⋊D67—82no—
673C22⋊D67—82no—
674C2×Dic67—21no—
675C2×Dic67—21no—
676C2×Dic67—21no—
677C2×Dic67—21no—
678C2×Dic67—21no—
679C2×Dic67—21no—
680C2×Dic67—21no—
681C2×Dic67—21no—
682C2×Dic67—21no—
683C2×Dic67—21no—
684C2×Dic67—21no—
685C2×Dic67—21no—
686C2×Dic67—21no—
687C2×Dic67—21no—
688C2×Dic67—21no—
689C2×Dic67—21no—
690C2×Dic67—21no—
691C2×Dic67—21no—
692C2×Dic67—21no—
693C2×Dic67—21no—
694C2×Dic67—21no—
695C2×Dic67—21no—
696C2×Dic67—21no—
697C2×Dic67—21no—
698C2×Dic67—21no—
699C2×Dic67—21no—
700C2×Dic67—21no—
701C2×Dic67—21no—
702C2×Dic67—21no—
703C2×Dic67—21no—
704C2×Dic67—21no—
705C2×Dic67—21no—
706C2×Dic67—21no—
707C2×Dic67—21no—
708C2×Dic67—21no—
709C2×Dic67—82no—
710C2×Dic67H(5,𝔽2)12yes—
711D268—44no—
712D268—44no—
713D268—82no—
714D268—82no—
715C4×D67—28no—
716C4×D67—44no—
717C4×D67—44no—
718C4×D67—82no—
719C4×D67—82no—
720C4×D67—82no—
721C4×D67—82no—
722C4×D67—82no—
723Dic134—82no—
724C22×C67—22no—
725C22×C67—22no—
726C22×C67—22no—
727C22×C67—41no—
728C22×C67—41no—
729C22×C67—41no—
730C22×C67—41no—
731C22×C67—41no—
732C22×C67—41no—
733C22×C67—41no—
734C22×C67—41no—
735C22×C67—41no—
736C22×C67—41no—
737C22×C67—41no—
738C22×C67C22×#4111yescharacteristic
739C22×C67C2×H(5,𝔽2)11yescharacteristic
740C22×C67C2×H(5,𝔽2)11yescharacteristic
741C22×C67C2×H(5,𝔽2)11yescharacteristic
742C22×C67C2×H(5,𝔽2)11yescharacteristic
743C22×C67C2×2−1+411yescharacteristic
744C22×C67#58511yescharacteristic
745C2×D67—22no—
746C2×D67—22no—
747C2×D67—22no—
748C2×D67—22no—
749C2×D67—22no—
750C2×D67—22no—
751C2×D67—22no—
752C2×D67—22no—
753C2×D67—22no—
754C2×D67—41no—
755C2×D67—41no—
756C2×D67—41no—
757C2×D67—41no—
758C2×D67—41no—
759C2×D67—41no—
760C2×D67—41no—
761C2×D67—41no—
762C2×D67—41no—
763C2×D67—41no—
764C2×D67—41no—
765C2×D67—41no—
766C2×D67—41no—
767C2×D67—41no—
768C2×D67—41no—
769C2×D67—41no—
770C2×D67—41no—
771C2×D67—41no—
772C2×D67—88no—
773C2×D67—88no—
774C2×D67#53914yes—
775C4×C67—22no—
776C4×C67—22no—
777C4×C67—41no—
778C4×C67—41no—
779C4×C67—41no—
780C4×C67—41no—
781C4×C67—41no—
782C4×C67—41no—
783C4×C67—41no—
784C4×C67—41no—
785C4×C67—41no—
786C4×C67—41no—
787C4×C67—41no—
788Dic67—22no—
789Dic67—41no—
790Dic67—41no—
791Dic67—41no—
792Dic67—41no—
793Dic67—41no—
794Dic67—41no—
795Dic67—41no—
796Dic67—41no—
797Dic67—41no—
798Dic67—41no—
799Dic67—41no—
800#36807—671nomaximal, Sylow
801C2×C67—42no—
802C2×C67—81no—
803C2×C67C2×#53911yescharacteristic
804C2×C67#349011yescharacteristic
805C2×C67#350511yescharacteristic
806C2×C67#353611yescharacteristic
807C2×C67#354211yescharacteristic
808C2×C67#354311yescharacteristic
809C2×C67#356111yescharacteristic
810D67—24no—
811D67—42no—
812D67—81no—
813D67—81no—
814#2852—671no—
815#2851—671no—
816#2796—671no—
817#2786—671no—
818#2757—671no—
819#2740—671no—
820#2737—671no—
821#2723—671no—
822#2711—671no—
823#2711—671no—
824#2707—671no—
825#2706—671no—
826#2705—671no—
827#2705—671no—
828#2696—671no—
829#2694D6711yescharacteristic, complemented
830#2691—671no—
831#2681—671no—
832#2626—671no—
833#2622—671no—
834#2480—671no—
835#2473—671no—
836#2449—671no—
837#2437—671no—
838#2418—671no—
839#2412—671no—
840#2410—671no—
841#2405—671no—
842#2321—671no—
843#2315—671no—
844C2×#390—671no—
845C67#3680711yescharacteristic, complemented, Sylow
846C23×D4—671no—
847C2×#126—671no—
848C2×#126—671no—
849C2×#125—671no—
850C2×#125C2×D6711yescharacteristic, complemented
851C2×#123—671no—
852C2×#123—671no—
853C2×#123—671no—
854C2×#123C2×D6711yescharacteristic
855C2×C22⋊Q8—671no—
856C2×C22⋊Q8—671no—
857C2×C22⋊Q8—671no—
858C2×#121—671no—
859C2×#121—671no—
860C2×#120—671no—
861C2×#120—671no—
862C2×C4×D4—671no—
863C22×C4⋊C4—671no—
864C22×C22⋊C4—671no—
865C22×C22⋊C4—671no—
866C22×C22⋊C4—671no—
867C22×C22⋊C4—671no—
868C22×C22⋊C4—671no—
869C22×C22⋊C4—671no—
870C22×C42—671no—
871#400—671no—
872#399—671no—
873#399—671no—
874#399—671no—
875#399C2×D6711yescharacteristic, complemented
876#399C2×D6711yescharacteristic, complemented
877#398—671no—
878#398—671no—
879#398—671no—
880#398C2×D6711yescharacteristic, complemented
881#397—671no—
882#397—671no—
883#397—671no—
884#397—671no—
885#397—671no—
886#397—671no—
887#397—671no—
888#397—671no—
889#397—671no—
890#397C2×D6711yescharacteristic, complemented
891#396—671no—
892#396—671no—
893#396—671no—
894#396—671no—
895#396—671no—
896#396—671no—
897#396—671no—
898#396C2×D6711yescharacteristic, complemented
899#395—671no—
900#394—671no—
901#394—671no—
902#394—671no—
903#394—671no—
904#394—671no—
905#394—671no—
906#394—671no—
907#394—671no—
908#394—671no—
909#394—671no—
910#394—671no—
911#394—671no—
912#394—671no—
913#394C2×D6711yescharacteristic
914#393—671no—
915#393—671no—
916#393—671no—
917#392—671no—
918#392—671no—
919#390—671no—
920#390—671no—
921#390—671no—
922#390—671no—
923#390—671no—
924#390—671no—
925#390—671no—
926#390—671no—
927#390—671no—
928#390C2×D6711yescharacteristic
929#389—671no—
930#389—671no—
931#389—671no—
932#389C2×D6711yescharacteristic, complemented
933#388—671no—
934#388—671no—
935#388—671no—
936#388—671no—
937#388—671no—
938#388—671no—
939#388—671no—
940#388—671no—
941#388—671no—
942#388—671no—
943#388C2×D6711yescharacteristic, complemented
944#388C2×D6711yescharacteristic, complemented
945#387—671no—
946#387—671no—
947#387—671no—
948#387—671no—
949#387—671no—
950#387—671no—
951#387—671no—
952#387—671no—
953#387—671no—
954#387C2×D6711yescharacteristic, complemented
955#386—671no—
956#386—671no—
957#386—671no—
958#386—671no—
959#386—671no—
960#386—671no—
961#386—671no—
962#386—671no—
963#386—671no—
964#386—671no—
965#386—671no—
966#386—671no—
967#385—671no—
968#385—671no—
969#385—671no—
970#385—671no—
971#385—671no—
972#385—671no—
973#385—671no—
974#385—671no—
975#385—671no—
976#385—671no—
977#385—671no—
978#385—671no—
979#385—671no—
980#385—671no—
981#385—671no—
982#385—671no—
983#385—671no—
984#385C2×D6711yescharacteristic, complemented
985#383—671no—
986#382—671no—
987#381—671no—
988#380—671no—
989#380—671no—
990#380—671no—
991#380—671no—
992#380—671no—
993#380—671no—
994#380—671no—
995#380C2×D6711yescharacteristic, complemented
996#379—671no—
997#379—671no—
998#379—671no—
999#379—671no—
1000C4×C22⋊C4—671no—
1001C25—671no—
1002C25—671no—
1003C22×Q8—671no—
1004C22×D4—2682no—
1005C22×D4—2682no—
1006C22×D4—671no—
1007C22×D4—671no—
1008C22×D4—671no—
1009C22×D4—671no—
1010C22×D4—671no—
1011C22×D4—671no—
1012C22×D4—671no—
1013C22×D4—671no—
1014C22×D4—1344no—
1015C22×D4C22×D6711yescharacteristic
1016C23×C4—671no—
1017C23×C4—671no—
1018C23×C4—671no—
1019C23×C4—671no—
1020C23×C4—671no—
1021C23×C4—671no—
1022C23×C4—671no—
1023C23×C4—671no—
1024C23×C4—671no—
1025C23×C4C22×D6711yescharacteristic
1026#126—2682no—
1027#126—2682no—
1028#125—42no—
1029#125—2682no—
1030#123—42no—
1031#123—2682no—
1032#123—2682no—
1033#123—2682no—
1034C22⋊Q8—2682no—
1035C22⋊Q8—2682no—
1036C22⋊Q8—2682no—
1037#121—2682no—
1038#121—2682no—
1039#120—2682no—
1040#120—1344no—
1041C4×D4—2682no—
1042C2×C4⋊C4—2682no—
1043C2×C4⋊C4—671no—
1044C2×C4⋊C4—671no—
1045C2×C4⋊C4—671no—
1046C2×C4⋊C4—671no—
1047C2×C4⋊C4—671no—
1048C2×C4⋊C4—671no—
1049C2×C4⋊C4—671no—
1050C2×C4⋊C4—671no—
1051C2×C4⋊C4—671no—
1052C2×C4⋊C4—671no—
1053C2×C4⋊C4—671no—
1054C2×C4⋊C4—671no—
1055C2×C4⋊C4—671no—
1056C2×C4⋊C4—671no—
1057C2×C4⋊C4—671no—
1058C2×C4⋊C4—671no—
1059C2×C4⋊C4—671no—
1060C2×C4⋊C4—671no—
1061C2×C4⋊C4—671no—
1062C2×C4⋊C4—671no—
1063C2×C4⋊C4—671no—
1064C2×C4⋊C4—671no—
1065C2×C4⋊C4C22×D6711yescharacteristic
1066C2×C4⋊C4C22×D6711yescharacteristic
1067C2×C4⋊C4C22×D6711yescharacteristic
1068C2×C4⋊C4C22×D6711yescharacteristic
1069C2×C4⋊C4C22×D6711yescharacteristic
1070C2×C4⋊C4C22×D6711yescharacteristic
1071C2×C4⋊C4C22×D6711yescharacteristic
1072C2×C4⋊C4C22×D6711yescharacteristic
1073C2×C4⋊C4C22×D6711yescharacteristic
1074C2×C4⋊C4C22×D6711yescharacteristic
1075C2×C4⋊C4C22×D6711yescharacteristic
1076C2×C4⋊C4C22×D6711yescharacteristic
1077C2×C22⋊C4—2682no—
1078C2×C22⋊C4—2682no—
1079C2×C22⋊C4—2682no—
1080C2×C22⋊C4—2682no—
1081C2×C22⋊C4—2682no—
1082C2×C22⋊C4—671no—
1083C2×C22⋊C4—671no—
1084C2×C22⋊C4—671no—
1085C2×C22⋊C4—671no—
1086C2×C22⋊C4—671no—
1087C2×C22⋊C4—671no—
1088C2×C22⋊C4—671no—
1089C2×C22⋊C4—671no—
1090C2×C22⋊C4—671no—
1091C2×C22⋊C4—671no—
1092C2×C22⋊C4—671no—
1093C2×C22⋊C4—671no—
1094C2×C22⋊C4—671no—
1095C2×C22⋊C4—671no—
1096C2×C22⋊C4—671no—
1097C2×C22⋊C4—671no—
1098C2×C22⋊C4—671no—
1099C2×C22⋊C4—671no—
1100C2×C22⋊C4—671no—
1101C2×C22⋊C4—671no—
1102C2×C22⋊C4—671no—
1103C2×C22⋊C4—671no—
1104C2×C22⋊C4—671no—
1105C2×C22⋊C4—671no—
1106C2×C22⋊C4—671no—
1107C2×C22⋊C4—671no—
1108C2×C22⋊C4—671no—
1109C2×C22⋊C4—671no—
1110C2×C22⋊C4—671no—
1111C2×C22⋊C4—671no—
1112C2×C22⋊C4—671no—
1113C2×C22⋊C4—671no—
1114C2×C22⋊C4—671no—
1115C2×C22⋊C4—671no—
1116C2×C22⋊C4—671no—
1117C2×C22⋊C4—671no—
1118C2×C22⋊C4—671no—
1119C2×C22⋊C4—671no—
1120C2×C22⋊C4—671no—
1121C2×C22⋊C4—671no—
1122C2×C22⋊C4—671no—
1123C2×C22⋊C4—671no—
1124C2×C22⋊C4—671no—
1125C2×C22⋊C4—671no—
1126C2×C22⋊C4—671no—
1127C2×C22⋊C4—1344no—
1128C2×C22⋊C4C22×D6711yescharacteristic
1129C2×C22⋊C4C22×D6711yescharacteristic
1130C2×C22⋊C4C22×D6711yescharacteristic
1131C2×C22⋊C4C22×D6711yescharacteristic
1132C2×C22⋊C4C22×D6711yescharacteristic
1133C2×C22⋊C4C22×D6711yescharacteristic
1134C2×C22⋊C4C22×D6711yescharacteristic
1135C2×C22⋊C4C22×D6711yescharacteristic
1136C2×C22⋊C4C22×D6711yescharacteristic
1137C2×C22⋊C4C22×D6711yescharacteristic
1138C2×C22⋊C4C22×D6711yescharacteristic
1139C2×C42—2682no—
1140C2×C42—671no—
1141C2×C42—671no—
1142C2×C42—671no—
1143C2×C42—671no—
1144C2×C42—671no—
1145C2×C42C22×D6711yescharacteristic
1146C2×C42C22×D6711yescharacteristic
1147#95—671no—
1148#95—671no—
1149#95—671no—
1150#95—671no—
1151#95—671no—
1152#95—671no—
1153#95—671no—
1154#95—671no—
1155#95—671no—
1156#95—671no—
1157#95—671no—
1158#95—671no—
1159#95—671no—
1160#95—671no—
1161#95—671no—
1162#95—671no—
1163#95—671no—
1164#95—671no—
1165#95—671no—
1166#95—671no—
1167#95—671no—
1168#95—671no—
1169#95—671no—
1170#95—671no—
1171#95—671no—
1172#95—671no—
1173#95—671no—
1174#95—671no—
1175#95C22×D6711yescharacteristic
1176#95C22×D6711yescharacteristic
1177#95C22×D6711yescharacteristic
1178#95C22×D6711yescharacteristic
1179#95C22×D6711yescharacteristic
1180#95C22×D6711yescharacteristic
1181#95C22×D6711yescharacteristic
1182#95C22×D6711yescharacteristic
1183C24—2681no—
1184C24—2681no—
1185C24—2681no—
1186C24—2681no—
1187C24—2681no—
1188C24—2681no—
1189C24—2681no—
1190C24—2681no—
1191C24—674no—
1192C24—671no—
1193C24—671no—
1194C24—671no—
1195C24—671no—
1196C24—1342no—
1197C24—1342no—
1198C24—1342no—
1199C24—1342no—
1200C24—1342no—
1201C24C23×D6711yescharacteristic
1202C24C23×D6711yescharacteristic
1203C2×Q8—2681no—
1204C2×Q8—2681no—
1205C2×Q8—2681no—
1206C2×D4—22no—
1207C2×D4—22no—
1208C2×D4—41no—
1209C2×D4—2681no—
1210C2×D4—2681no—
1211C2×D4—2681no—
1212C2×D4—2681no—
1213C2×D4—2681no—
1214C2×D4—2681no—
1215C2×D4—26816no—
1216C2×D4—2681no—
1217C2×D4—2681no—
1218C2×D4—2681no—
1219C2×D4—2681no—
1220C2×D4—2681no—
1221C2×D4—2681no—
1222C2×D4—2681no—
1223C2×D4—1342no—
1224C2×D4—1342no—
1225C2×D4—1342no—
1226C2×D4—1342no—
1227C2×D4—1342no—
1228C2×D4—1342no—
1229C2×D4—1342no—
1230C2×D4—1342no—
1231C2×D4—1342no—
1232C2×D4—1342no—
1233C2×D4—1342no—
1234C22×C4—22no—
1235C22×C4—41no—
1236C22×C4—41no—
1237C22×C4—2681no—
1238C22×C4—2681no—
1239C22×C4—2681no—
1240C22×C4—2681no—
1241C22×C4—2681no—
1242C22×C4—2681no—
1243C22×C4—2681no—
1244C22×C4—2681no—
1245C22×C4—2681no—
1246C22×C4—2681no—
1247C22×C4—2681no—
1248C22×C4—2681no—
1249C22×C4—2681no—
1250C22×C4—2681no—
1251C22×C4—2681no—
1252C22×C4—2681no—
1253C22×C4—2681no—
1254C22×C4—2681no—
1255C22×C4—671no—
1256C22×C4—671no—
1257C22×C4—671no—
1258C22×C4—671no—
1259C22×C4—671no—
1260C22×C4—671no—
1261C22×C4—671no—
1262C22×C4—671no—
1263C22×C4—671no—
1264C22×C4—671no—
1265C22×C4—671no—
1266C22×C4—671no—
1267C22×C4—1342no—
1268C22×C4—1342no—
1269C22×C4—1342no—
1270C22×C4—1342no—
1271C22×C4—1342no—
1272C22×C4—1342no—
1273C22×C4—1342no—
1274C22×C4—1342no—
1275C22×C4—1342no—
1276C22×C4C23×D6711yescharacteristic
1277C22×C4C23×D6711yescharacteristic
1278C22×C4C23×D6711yescharacteristic
1279C22×C4C23×D6711yescharacteristic
1280C22×C4C23×D6711yescharacteristic
1281C22×C4C23×D6711yescharacteristic
1282C22×C4C23×D6711yescharacteristic
1283C22×C4C23×D6711yescharacteristic
1284C22×C4C23×D6711yescharacteristic
1285C22×C4C23×D6711yescharacteristic
1286C22×C4C23×D6711yescharacteristic
1287C22×C4C23×D6711yescharacteristic
1288C22×C4C23×D6711yescharacteristic
1289C4⋊C4—22no—
1290C4⋊C4—22no—
1291C4⋊C4—22no—
1292C4⋊C4—22no—
1293C4⋊C4—22no—
1294C4⋊C4—41no—
1295C4⋊C4—41no—
1296C4⋊C4—41no—
1297C4⋊C4—41no—
1298C4⋊C4—41no—
1299C4⋊C4—41no—
1300C4⋊C4—41no—
1301C4⋊C4—2681no—
1302C4⋊C4—2681no—
1303C4⋊C4—2681no—
1304C4⋊C4—2681no—
1305C4⋊C4—2681no—
1306C4⋊C4—2681no—
1307C4⋊C4—2681no—
1308C4⋊C4—2681no—
1309C4⋊C4—2681no—
1310C4⋊C4—2681no—
1311C4⋊C4—2681no—
1312C4⋊C4—2681no—
1313C4⋊C4—2681no—
1314C4⋊C4—2681no—
1315C4⋊C4—2681no—
1316C4⋊C4—2681no—
1317C4⋊C4—1342no—
1318C4⋊C4—1342no—
1319C4⋊C4—1342no—
1320C4⋊C4—1342no—
1321C4⋊C4—1342no—
1322C4⋊C4—1342no—
1323C22⋊C4—22no—
1324C22⋊C4—22no—
1325C22⋊C4—22no—
1326C22⋊C4—41no—
1327C22⋊C4—41no—
1328C22⋊C4—41no—
1329C22⋊C4—41no—
1330C22⋊C4—41no—
1331C22⋊C4—41no—
1332C22⋊C4—41no—
1333C22⋊C4—41no—
1334C22⋊C4—2681no—
1335C22⋊C4—2681no—
1336C22⋊C4—2681no—
1337C22⋊C4—2681no—
1338C22⋊C4—2681no—
1339C22⋊C4—2681no—
1340C22⋊C4—2681no—
1341C22⋊C4—2681no—
1342C22⋊C4—2681no—
1343C22⋊C4—2681no—
1344C22⋊C4—2681no—
1345C22⋊C4—2681no—
1346C22⋊C4—2681no—
1347C22⋊C4—2681no—
1348C22⋊C4—2681no—
1349C22⋊C4—2681no—
1350C22⋊C4—2681no—
1351C22⋊C4—2681no—
1352C22⋊C4—2681no—
1353C22⋊C4—2681no—
1354C22⋊C4—2681no—
1355C22⋊C4—2681no—
1356C22⋊C4—2681no—
1357C22⋊C4—2681no—
1358C22⋊C4—2681no—
1359C22⋊C4—2681no—
1360C22⋊C4—2681no—
1361C22⋊C4—2681no—
1362C22⋊C4—2681no—
1363C22⋊C4—2681no—
1364C22⋊C4—1342no—
1365C22⋊C4—1342no—
1366C22⋊C4—1342no—
1367C22⋊C4—1342no—
1368C22⋊C4—1342no—
1369C22⋊C4—1342no—
1370C22⋊C4—1342no—
1371C22⋊C4—1342no—
1372C22⋊C4—1342no—
1373C22⋊C4—1342no—
1374C22⋊C4—1342no—
1375C22⋊C4—1342no—
1376C22⋊C4—1342no—
1377C22⋊C4—1342no—
1378C22⋊C4—1342no—
1379C42—41no—
1380C42—41no—
1381C42—2681no—
1382C42—2681no—
1383C42—2681no—
1384C42—1342no—
1385C42—1342no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—2684no—
1400C23—2684no—
1401C23—2684no—
1402C23—2684no—
1403C23—2684no—
1404C23—5362no—
1405C23—5362no—
1406C23—5362no—
1407C23—5362no—
1408C23—5362no—
1409C23—5362no—
1410C23—5362no—
1411C23—5362no—
1412C23—672no—
1413C23—672no—
1414C23—672no—
1415C23—672no—
1416C23—1348no—
1417C23—1341no—
1418C23—1341no—
1419C23—1341no—
1420C23—1341no—
1421C23—1341no—
1422C23—1341no—
1423C23—1341no—
1424C23—1341no—
1425C23—1341no—
1426C23—1341no—
1427C23—1341no—
1428C23—1341no—
1429C23—1341no—
1430C23—1341no—
1431C23—1341no—
1432C23—1341no—
1433C23—1341no—
1434C23—1341no—
1435C23—1341no—
1436C23—1341no—
1437C23—1341no—
1438C23—1341no—
1439C23—1341no—
1440C23—1341no—
1441C23#41×D6712yes—
1442C23C24×D6711yescharacteristic
1443Q8—5362no—
1444D4—44no—
1445D4—2684no—
1446D4—2684no—
1447D4—2684no—
1448D4—2684no—
1449D4—5362no—
1450D4—5362no—
1451D4—5362no—
1452D4—5362no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—82no—
1491C2×C4—2684no—
1492C2×C4—2684no—
1493C2×C4—5362no—
1494C2×C4—5362no—
1495C2×C4—5362no—
1496C2×C4—5362no—
1497C2×C4—5362no—
1498C2×C4—5362no—
1499C2×C4—672no—
1500C2×C4—1348no—
1501C2×C4—1341no—
1502C2×C4—1341no—
1503C2×C4—1341no—
1504C2×C4—1341no—
1505C2×C4—1341no—
1506C2×C4—1341no—
1507C2×C4—1341no—
1508C2×C4—1341no—
1509C2×C4—1341no—
1510C2×C4—1341no—
1511C2×C4—1341no—
1512C2×C4—1341no—
1513C2×C4—1341no—
1514C2×C4—1341no—
1515C2×C4—1341no—
1516C2×C4—1341no—
1517C2×C4—1341no—
1518C2×C4—1341no—
1519C2×C4—1341no—
1520C2×C4—1341no—
1521C2×C4—1341no—
1522C2×C4—1341no—
1523C2×C4—1341no—
1524C2×C4—1341no—
1525C2×C4—1341no—
1526C2×C4—1341no—
1527C2×C4—1341no—
1528C2×C4—1341no—
1529C2×C4—1341no—
1530C2×C4—1341no—
1531C2×C4—1341no—
1532C2×C4—1341no—
1533C2×C4—1341no—
1534C2×C4—1341no—
1535C2×C4—1341no—
1536C2×C4#1452408812yes—
1537C2×C4#1452408912yes—
1538C22—22no—
1539C22—22no—
1540C22—22no—
1541C22—41no—
1542C22—41no—
1543C22—41no—
1544C22—41no—
1545C22—41no—
1546C22—41no—
1547C22—41no—
1548C22—41no—
1549C22—41no—
1550C22—41no—
1551C22—41no—
1552C22—2681no—
1553C22—2681no—
1554C22—2681no—
1555C22—2681no—
1556C22—2681no—
1557C22—2681no—
1558C22—2681no—
1559C22—2681no—
1560C22—2681no—
1561C22—2681no—
1562C22—2681no—
1563C22—2681no—
1564C22—2681no—
1565C22—2681no—
1566C22—2681no—
1567C22—2681no—
1568C22—2681no—
1569C22—2681no—
1570C22—5368no—
1571C22—5368no—
1572C22—674no—
1573C22—1342no—
1574C22—1342no—
1575C22—1342no—
1576C22—1342no—
1577C22—1342no—
1578C22—1342no—
1579C22—1342no—
1580C22—1342no—
1581C22—1342no—
1582C22C2×#41×D6711yescharacteristic
1583C22H(5,𝔽2)×D6711yescharacteristic
1584C22H(5,𝔽2)×D6711yescharacteristic
1585C22C2×#1452408811yescharacteristic
1586C22C2×#1452408911yescharacteristic
1587C222−1+4×D6711yescharacteristic
1588C22#1686423311yescharacteristic
1589C4—22no—
1590C4—22no—
1591C4—41no—
1592C4—41no—
1593C4—41no—
1594C4—41no—
1595C4—41no—
1596C4—41no—
1597C4—41no—
1598C4—41no—
1599C4—41no—
1600C4—41no—
1601C4—41no—
1602C4—2681no—
1603C4—2681no—
1604C4—2681no—
1605C4—2681no—
1606C4—2681no—
1607C4—2681no—
1608C4—2681no—
1609C4—2681no—
1610C4—2681no—
1611C4—2681no—
1612C4—2681no—
1613C4—1342no—
1614C2—42no—
1615C2—81no—
1616C2—2682no—
1617C2—5361no—
1618C2—5361no—
1619C2—1344no—
1620C2#539×D6711yescharacteristic
1621C2#2257389111yescharacteristic
1622C2#2257404911yescharacteristic
1623C2#2257443311yescharacteristic
1624C2#2257452211yescharacteristic
1625C2#2257453311yescharacteristic
1626C2#2257477011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D67
commutator, socle, cosocleC23×C67C25
FittingC67×#2694C2
prime radical#22563578C2
hypercenter#2694D67
hypocenterC67#36807
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C23 ◁ #2694

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #22568527C2semidirect
2. #22568518C2semidirect
3. #22568054C2semidirect
4. #22567931C2semidirect
5. #22567545C2semidirect
6. #22567311C2semidirect
7. #22567258C2semidirect
8. #22567121C2semidirect
9. #22566963C2semidirect
10. #22566962C2semidirect
11. #22566916C2semidirect
12. #22566896C2semidirect
13. #22566882C2semidirect
14. #22566877C2semidirect
15. #22566755C2semidirect
16. #22566696C2semidirect
17. #22566556C2semidirect
18. #22566019C2semidirect
19. #22565983C2semidirect
20. #22564453C2semidirect
21. #22564346C2semidirect
22. #22564013C2semidirect
23. #22563876C2semidirect
24. #22563674C2semidirect
25. #22563603C2semidirect
27. #22563533C2semidirect
28. #22562862C2semidirect
29. #22562822C2semidirect
30. #390×D67C2semidirect
31. C67×#2694C2semidirect
33. C2×#14524038C22semidirect
34. C2×#14524036C22semidirect
35. C2×#14524034C22semidirect
36. C2×#14524028C22semidirect
37. C2×#14524027C22semidirect
39. C2×#14524023C22semidirect
41. C2×#14524021C22semidirect
55. #16863335C22semidirect
56. #16863332C22semidirect
57. #16863331C22semidirect
58. #16863331C22semidirect
59. #16863329C22semidirect
60. #16863327C22semidirect
61. #16863326C22semidirect
62. #16863325C22semidirect
63. #16863324C22semidirect
64. #16863323C22semidirect
65. #16863323C22semidirect
66. #16863323C22semidirect
67. #16863323C22semidirect
68. #16863322C22semidirect
69. #16863321C22semidirect
70. #16863321C22semidirect
71. #16863320C22semidirect
72. #16863319C22semidirect
73. #16863319C22semidirect
74. #16863319C22semidirect
75. #16863318C22semidirect
76. #16863318C22semidirect
77. #16863318C22semidirect
78. #16863316C22semidirect
79. #16863314C22semidirect
82. #16863313C22semidirect
83. #16863313C22semidirect
84. #16863313C22semidirect
85. #16863313C22semidirect
86. #16863312C22semidirect
87. #16863312C22semidirect
91. #16863311C22semidirect
92. #16863309C22semidirect
93. #16863308C22semidirect
94. #16863308C22semidirect
99. #16863298C22semidirect
105. #16863296C22semidirect
106. #16863294C22semidirect
107. #16863293C22semidirect
108. #16863291C22semidirect
109. #16863289C22semidirect
110. #16863288C22semidirect
111. #16863288C22semidirect
112. #16863287C22semidirect
113. #16863287C22semidirect
114. #16863286C22semidirect
115. #16863286C22semidirect
116. #16863285C22semidirect
117. #16863285C22semidirect
118. #16863284C22semidirect
119. #16863283C22semidirect
120. #16863282C22semidirect
121. #16863282C22semidirect
122. #16863282C22semidirect
123. #16863280C22semidirect
124. #16863279C22semidirect
125. #16863278C22semidirect
126. #16863278C22semidirect
127. #16863278C22semidirect
129. #16863275C22semidirect
135. #16863274C22semidirect
138. #16863272C22semidirect
139. #16863272C22semidirect
144. #16863270C22semidirect
145. #16863270C22semidirect
146. #16863270C22semidirect
153. #16863267C22semidirect
154. #16863267C22semidirect
155. #16863267C22semidirect
156. #16863267C22semidirect
157. #16863263C22semidirect
158. #16863261C22semidirect
159. #16863257C22semidirect
160. #16863256C22semidirect
161. #16863254C22semidirect
162. #16863254C22semidirect
166. #16863253C22semidirect
172. C2×#125×C67C22semidirect
174. #399×C67C22semidirect
175. #399×C67C22semidirect
176. #398×C67C22semidirect
177. #397×C67C22semidirect
178. #396×C67C22semidirect
181. #389×C67C22semidirect
182. #388×C67C22semidirect
183. #388×C67C22semidirect
184. #387×C67C22semidirect
185. #385×C67C22semidirect
186. #380×C67C22semidirect
829. #2694D67semidirect
845. C67#36807semidirect
850. C2×#125C2×D67semidirect
875. #399C2×D67semidirect
876. #399C2×D67semidirect
880. #398C2×D67semidirect
890. #397C2×D67semidirect
898. #396C2×D67semidirect
932. #389C2×D67semidirect
943. #388C2×D67semidirect
944. #388C2×D67semidirect
954. #387C2×D67semidirect
984. #385C2×D67semidirect
995. #380C2×D67semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#225685272
#225685182
#225680542
#225679312
#225675452
#225673112
#225672582
#225671212
#225669632
#225669622
#225669162
#225668962
#225668822
#225668772
#225667552
#225666962
#225665562
#225660192
#225659832
#225644532
#225643462
#225640132
#225638762
#225636742
#225636032
#225635782
#225635332
#225628622
#225628222
#390×D672
C67×#26942
#3680767